Stochastic Models That Separate Fractal Dimension and the Hurst Effect

摘要: Fractal behavior and long-range dependence have been observed in an astonishing number of physical, biological, geological, socioeconomic systems. Time series, profiles, surfaces characterized by their fractal dimension, a measure roughness, the Hurst coefficient, long-memory dependence. Both phenomena modeled explained self-affine random functions, such as fractional Gaussian noise Brownian motion. The assumption statistical self-affinity implies linear relationship between dimension coefficient thereby links two phenomena. This article introduces stochastic models that allow for any combination coefficient. Associated software synthesis images with arbitrary, prespecified properties power-law correlations is available. new suggest test assesses coupling decoupling local global behavior.